Question

if cot 0-1/cot 0+1 = 1-√3/1+√3 then find the acute angle 0 [ here 0 is theta]{here / means divide }( ans is 60⁰)​

Answer 1

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$\frac{cot \alpha - 1}{cot \alpha + 1} = \frac{1 - \sqrt{3} }{1 + \sqrt{3} } \\ using \: componendo \: dividendo \: method \\ \frac{(cot \alpha - 1) + (cot \alpha + 1)}{(cot \alpha - 1) - (cot \alpha + 1)} = \frac{(1 - \sqrt{3} ) + (1 + \sqrt{3} )}{(1 - \sqrt{3}) - (1 + \sqrt{3} ) } \\ \frac{2cot \alpha }{ - 2} = \frac{2}{ - 2 \sqrt{3} } \\ cot \alpha = \frac{1}{ \sqrt{3} } \\ \alpha = \frac{\pi}{3}$